Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Covering by complements of subspaces, II

Author(s): W. Edwin Clark; Boris Shekhtman
Journal: Proc. Amer. Math. Soc. 125 (1997), 251-254.
MSC (1991): Primary 51A99; Secondary 14N10, 15A75, 15A99
MathSciNet review: 1346967
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Abstract: Let $V$ be an $n$ -dimensional vector space over an algebraically closed field $K$ . Define $\gamma (k,n,K)$ to be the least positive integer $t$ for which there exists a family $E_{1}, E_{2}, \dots , E_{t}$ of $k$ -dimensional subspaces of $V$ such that every $(n-k)$ -dimensional subspace $F$ of $V$ has at least one complement among the $E_{i}$ 's. Using algebraic geometry we prove that $\gamma (k,n,K) = k(n-k) +1$ .

References:

1.: W. Edwin Clark and Boris Shekhtman, Covering by complements of subspaces, Linear and Multilinear Algebra 40 (1995), 1-13. CMP 96:08
2.: -, Domination numbers of q-analogues of Kneser graphs, Bulletin of the Institute of Combinatorics and its Applications (to appear).
3.: J. Harris, Algebraic Geometry, Springer-Verlag, 1992. MR 93j:14001

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